Question: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 6x - 1$ and $ JT = 3x + 14$ Find $CT$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {6x - 1} = {3x + 14}$ Solve for $x$ $ 3x = 15$ $ x = 5$ Substitute $5$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 6({5}) - 1$ $ JT = 3({5}) + 14$ $ CJ = 30 - 1$ $ JT = 15 + 14$ $ CJ = 29$ $ JT = 29$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {29} + {29}$ $ CT = 58$